Ultrasonic Meter Employing Two or More Dissimilar Chordal Multipath Integration Methods in One Body

ABSTRACT

A system and method to detect and quantify integration errors in a transit time ultrasonic flow meter uses dissimilar integration methods or schemes employed simultaneously. In a preferred embodiment, a number of chordal paths are arranged in a single meter body such that at least two dissimilar chordal integration schemes can be used to determine the flow rate. At least one of the chordal paths is common to both integration schemes. The total number of chordal paths needed in any chordal measurement plane is less than the sum of the chordal paths used in each of the integration schemes (as is the sum of the planes), thereby reducing hardware requirements.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation application which claims priority to U.S. patentapplication Ser. No. 14/980,007 filed Dec. 28, 2015, the contents ofwhich are incorporated by reference.

BACKGROUND OF THE INVENTION

This invention generally relates to self-checking flow meters based onthe principles of ultrasonic transit time measurement. Morespecifically, the invention relates to a self-checking, transit timeultrasonic flowmeter which uses two or more chordal integration methodswithin a single meter body.

Because transit time ultrasonic flowmeters are capable of high accuracyperformance over a wide range of application conditions, the meters havebeen adopted in applications ranging from custody transfer ofhydrocarbons to measurement of nuclear feed water flows.

To achieve their high accuracy, transit time ultrasonic flowmeterscommonly employ multiple pairs of transducers to infer velocity on anumber of discrete chordal planes. The velocity measurements can then becombined, along with information on geometry, to produce a measure ofvolumetric flowrate, Q.

For the purpose of this disclosure, a path is an intended route ofultrasound transmission through the fluid between two transducers. Achordal path (or chord) is a path confined to a single chordal plane. Achordal plane is a plane that intersects two points on the boundary of aconduit and extends in a direction that is parallel with the centralaxis of the conduit.

Because velocity is continuous but can only be sampled on a number ofdiscrete paths though the conduit, the meters can be prone tointegration error. Because of this error, the measured flowrate derivedfrom the velocity on multiple paths is not equal to the true flowrate.Even if the individual chordal path velocity measurements made by themeter have no intrinsic errors, identifying or quantifying theintegration errors can be quite challenging. One way of identifying theintegration error is to compare, using chordal integration methods, flowrate measurement results from different chordal integration methods in asingle meter.

Chordal integration methods have been used in transit time ultrasonicflowmeters since the late 1960's. By choosing the path locations andcombining the individual velocity measurements linearly according torules for numerical integration, the result can represent the velocityintegrated or averaged over the cross-section, and hence the volumetricflowrate, i.e.

$\overset{\_}{v} = {\sum\limits_{i = 1}^{N}\; {w_{i}{v\left( h_{i} \right)}}}$$Q = {{\overset{\_}{v}A} = {A{\sum\limits_{i = 1}^{N}\; {w_{i}{v\left( h_{i} \right)}}}}}$

where Q is volumetric flowrate, v is average velocity, A iscross-sectional area, v(h_(i)) is the path velocity at distance h_(i),and w_(i) is the factor used to weight the velocity measurement beforesummation as illustrated in FIG. 1. Chord locations (h_(i)) andweighting factors (w_(i)) based on the rules of Gaussian integration arecommonly chosen, based on either Legendre or Jacobi polynomials.Alternative integration schemes such as Chebyshev or Lobatto methods canalso be applied.

More recently ultrasonic flow measurement methods have been developedwhich make use of two independent measurement systems in order toattempt to identify measurement errors. Examples include the combinationof a 4-path chordal measurement with a single-path chordal measurement(see e.g. FIG. 3) and the combination of two 4-path chordal measurements(see e.g. FIG. 4). Although these new methods are generally better atdetecting measurement errors than their predecessor methods, they areprone to other operating problems and are deficient when it comes todetection of integration errors.

In the case of the first method, the single-path measurement is muchmore sensitive to velocity profile changes than the 4-path chordalmeasurement. Therefore, the meter has a tendency to trigger an alarm ata level where the 4-path chordal measurement is still accurate.

The second method is potentially subject to “common mode” errors.Because the two 4-path chordal measurement systems are similar, anyerror common to both systems can be equal and, therefore, go undetected.To avoid this problem it is desirable to use two or more dissimilarmulti-path chordal integration methods and that, in turn, increasesoverall hardware requirements. For example, to compare a 3-chordintegration with a 4-chord integration, the meter body is required tohave measurement paths in 7 chordal planes in total.

A need exists for an transit time ultrasonic flow meter that canaccurately and reliably detect integration errors, avoids thedeficiencies of the prior art methods, and reduces the overall hardwarerequirements that the use of dissimilar chordal measurement systemspresents.

SUMMARY OF THE INVENTION

A system and method for use in a transit time ultrasonic flow meter usesdissimilar integration methods or schemes employed simultaneously in aneffort to detect and quantify integration errors. In a preferredembodiment, a number of chordal paths are arranged in a single meterbody such that at least two dissimilar chordal integration methods canbe used to determine the flow rate. At least one of the chordal paths(and therefore at least one of the chordal planes) is common to bothintegration methods so that the total number of chordal paths needed isless than the sum of the chordal paths used in each of the integrationmethods (as is the sum of the planes), thereby reducing hardwarerequirements.

Multiple paths can be used per chordal measurement plane. By way of anon-limiting example, a 4-chord integration scheme and a 3-chord schemecould be used, each scheme having two paths per chordal measurementplane with the outermost chords shared between the two differentschemes. Eight paths are used in the 4-chord scheme and six in the3-chord scheme. However, rather than 14 paths being used, the sharingresults in a total of five chordal measurement planes and ten paths (twopaths per plane) in total.

In a preferred embodiment of the method, a non-transitory computerreadable medium with computer instructions stored thereon executed by aprocessor performs a first chordal integration scheme and a seconddifferent chordal integration scheme, at least one chordal path beingcommon to the first and second different chordal integration schemes.The one chordal path lies in a discrete chordal measurement plane acrossa conduit section of a meter body and the total number of chordal pathsis less than a sum of the chordal paths used in the first and seconddifferent chordal integration schemes.

The method can include the step of selecting the path locations andweighting factors of the first or second chordal integration scheme tocorrespond with predefined abscissa and weights of a documentednumerical integration scheme. Or the method can include the step ofselecting the path locations of the first or second chordal integrationindependent of documented numerical integration schemes with predefinedabscissa, and then determining weighting factors to correspond withthose selected locations.

The method can further include the step of selecting a location of theat least one chordal path and weighing factors that correspond with anabscissa and weights of at least one of the first and second differentchordal integration schemes. Or, the method can include the step ofselecting a location of the at least one chordal path locationindependent of an abscissa of at least one of the first and seconddifferent chordal integration schemes and calculating weighing factorsaccordingly.

Either the first or second different chordal integration schemes can bean odd-numbered integration scheme and the other one an even-numberedintegration scheme. Both schemes could also be odd-numbered oreven-numbered.

In a preferred embodiment of the system, a meter body houses multipleultrasonic transducers that form the chordal paths and a non-transitorycomputer readable medium with computer executable instructions executedby a processor includes a first chordal integration scheme and a seconddifferent chordal integration scheme, at least one chordal path beingcommon to the first and second different chordal integration schemes.The chordal measurement plane can contain two or more chordal pathsarranged at different angles to a conduit axis such that a chordalvelocity measurement in each chordal measurement plane can be made thatis substantially independent of non-axial flow.

The first chordal integration scheme and the second different chordalintegration scheme can use two subsets of chordal measurement planeseach with a summation that uses weighting factors that are dissimilar.One of the chordal integration schemes can be an odd-numberedintegration scheme and another of the chordal integration schemes can bean even-numbered integration scheme.

Objectives of the system and method include accurately and reliablydetecting integration errors, avoiding the deficiencies of the prior artmethods, and reducing the overall hardware requirements that the use ofdissimilar chordal measurement systems presents.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a chordal integration method showing chord locationswith h spacing as per the integration method. Velocity is measured oneach chord, multiplied by weighting factors as per the integrationmethod, and then summed.

FIG. 2 is a schematic illustrating a preferred embodiment of a systemused in connection with the method of FIGS. 7 and 8.

FIG. 3 (prior art) is a schematic illustrating a flow meter withultrasonic transducers defining multiple chordal paths. There are twoindependent subsets of paths: one set of four arranged as per a chordalintegration flow measurement method and a separate single path flowmeasurement. Transducer data are transmitted to a computing devicehaving computer readable media with executable instructions of apreferred embodiment of the integration method (see FIG. 1).

FIG. 4 (prior art) is a schematic illustrating multiple chordal pathsused to make two 4-path flow measurements in a single meter body. Inthis case the chordal integration scheme (spacing and weighting factors)for each 4-path measurement is the same as the other, and each chordalmeasurement uses an independent subset of paths.

FIG. 5 is a graph hydraulic correction factors from a fully developed(Reichardt) flow profile for various integration schemes.

FIG. 6 is a graph of chord spacing (abscissa) for 3-chordAnti-Gauss-Jacobian and 4-chord Gauss-Legendre integration schemes.

FIG. 7 is a graph of integration error for the 4-chord scheme, plottedversus the difference between the 3- and 4-chord integrations.

FIG. 8 is a graph of integration error for the 4-chord scheme, plottedversus the difference between a single diameter measurement and the4-chord integration scheme.

FIG. 9 is a schematic illustrating three- and four-chord measurementschemes in a single body.

FIG. 10 (prior art) is a non-limiting example of an ultrasonic flowmeter that can be adapted to include the two or more dissimilar chordalmultipath integration methods in one body. In this example, the meter isan 8-path CALDON™ ultrasonic flow meter (Cameron International Corp.,Houston, Tex.).

ELEMENTS AND NUMBERING USED IN THE DRAWINGS

-   -   10 Flow meter system having two or more dissimilar chordal        integration methods    -   20 Signal processing means (computational electronics)    -   21 Acoustic processing unit (“APU”)    -   25 Central processing control and display unit    -   27 Microprocessor    -   29 Input/output with software (non-transitory computer readable        medium)    -   30 Chordal path    -   40 Flow meter body

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A system and method for detecting and estimating integration errorassociated with the use of an ultrasonic flowrate meter includes two ormore dissimilar chordal multipath integration methods employed in asingle meter body. The system differs from prior art systems and methodsin that it compares two or more sets of overlapping chordal input datato detect and quantify the error. Because dissimilar integration methodsare used, the comparison is less prone to production of false alarms.Additionally, the system does not require that the total number ofchordal measurement planes be equal to the sum of the number of chordalplanes used in each integration. Because the total number of planes canbe less than the total number of chordal velocity inputs to theplurality of integration schemes, overall hardware requirements arereduced.

One example of how this is accomplished is to employ one even-numberedand one odd-numbered integration method or scheme of different typewhere at least one chordal path (and therefore at least one chordalplane) is shared between the two integration schemes. This methodreduces the likelihood of a false alarm and reduces hardwarerequirements by constructing and operating the meter in such a way thattwo separate integrations are performed using overlapping subsets ofchordal measurement data. For example, where a conventional approachwould require seven chordal measurement planes in total to compare 3-and 4-chord integration schemes, only five chordal measurement planes intotal are required here, with three of five chords being used for afirst integration routine and four of five chords being used for asecond integration routine. In a similar way, a combination of a 4-chordintegration scheme with a 5-chord integration scheme can be achievedusing only five chords when all chords are used in the 5-chord schemeand all but one in a dissimilar 4-chord scheme.

Referring to FIG. 2, the system 10 can be used as part of the signalprocessing means 20 of an ultrasonic flow meter having two or morechordal measurement planes 30 within the meter body 40. This type ofmeter typically includes transducers arranged upstream and downstream ofone another in pitch-and-catch relationship to send acoustic energyalong an acoustic path through the fluid flowing in a conduit (see e.g.FIGS. 3 and 4). The signal processing means 20 determines the transittimes for upstream and downstream signal transmission and uses thosemeasured upstream and downstream transit times in combination with otherinputs to calculate the velocity in each measurement plane and to inferthe flow rate of the fluid.

The signal processing means or computational electronics 20 includes atransmitter or acoustic processing unit (“APU”) 21 and a centralprocessing, control and display unit 25 (see FIG. 2). Commonly, the flowmeter could have the electronics mounted directly to the meter body, andthe functions of the APU 21 and central processing, control and displayunit 25 could be separate or combined. The APU 21 controls thetransmission and reception of the ultrasonic signals to and from thetransducers. The central processing, control and display unit 25, whichincludes a microprocessor 27 and I/O with software 29 (and memory),typically employs Gaussian integration schemes to process the transittime measurements along the various chordal paths 30 from the APU 21 andcalculate flow rate. The central processing, control and display unit 25can also function as the user interface.

Note there can be two sets of computational electronics attached to thetransducers with one or more of the paths and the transducers sharedbetween these electronics with one performing the first integrationscheme and another performing the second integration scheme. In thisembodiment, communication is required between the two sets ofcomputational electronics so that each set does not use the sametransducers at the same time.

A non-limiting example of this type of meter is a CALDON™ ultrasonicflow meter (s). The CALDON™ meter uses a compact transmitter enclosurethat can be integrally mounted to the meter body or remote pipe mounted(see FIG. 10). Within the meter body are multiple pairs of fullyintegrated piezoelectric ultrasonic transducers forming acousticmeasurement paths in multiple chordal planes. These paths typicallycross the flow stream at an angle of between 45 and 65 degrees so thatthere is a difference in the transit time of the ultrasonic signals,depending on whether the sound pulse is traveling with or against thedirection of flow. The difference in transit times is measured alongeach path. The meter's electronics infer velocity on each chord andperform an integration of axial velocity to compute an output ofvolumetric flow rate. In one preferred design, paths are arranged incrossed pairs in each chordal measurement plane. This arrangement ofacoustic paths make the axial velocity calculation substantially immuneto the effects of non-axial flow and eliminates the need for an upstreamflow conditioner. By eliminating the interfering effect of non-axialflow the crossed-pair design enables the integration method to functionproperly and reducing the requirement for long upstream lengths ofstraight pipe.

Referring now to FIG. 5, integration of the Reichardt profile bywell-known methods shows that a 3-chord Anti-Gauss-Jacobian(“Anti-Gauss”) integration gives a comparable linearity to that of a4-chord Jacobian integration. This result shows that the 3-chordAnti-Gauss integration is useful for accurate flow rate measurements.Additionally, the outer chords of the 3-chord Anti-Gauss integration arepositioned at almost the same location as the outer chords of a 4-chordGauss-Legendre integration (see FIG. 6).

Because of this, an arrangement of five chordal measurement planes intotal can be used to closely approximate mathematically prescribedintegration schemes for both 3- and 4-chord integrations. For example,the 3-chord Anti-Gauss and the 4-chord Legendre can both be realized byadding a single diametric chordal measurement plane to the 4-chordLegendre arrangement. In this case the chord locations normalized to thepipe diameter for the 4-chord Legendre scheme are −0.861136, −0.339981,0.339981 and 0.861136. For the 3-chord Anti-Gauss scheme the chordlocations are −0.866025, 0 and 0.866025. The five-chord scheme cantherefore be realized by placing the two outermost chords at between−0.861136 and −0.866025 and between +0.861136 and +0.866025, e.g.−0.863581 and +0.863581. The corresponding weighting factors for thevelocities measured on each plane would then be applied as given inTable 1 below.

TABLE 1 Weighting Factors. Integration method 1 Integration method 2weighting factors weighting factors Chord (three chord (four chordnumber Chord location integration) integration) 1 −0.863581 0.1666670.112580 2 −0.339981 0.390438 3 0 0.666667 4 0.339981 0.390438 50.863581 0.166667 0.112580

FIG. 7 provides an example of how this system can be implemented on thesoftware of the central processing, control and display unit and used aspart of the signal processing means of an ultrasonic flow meter. For thetwo distorted flow profiles shown, the 4-chord integration error(y-axis) is plotted versus the difference between the 3- and 4-chordintegrations for various orientations of the profile with rotation ofthe flow profile in 5 degree steps from 0 to 180 degrees. Theintegration error in the 4-chord integration is approximately equal to⅕th of the difference between the 3- and 4-chord integrations, thusallowing the detection and estimation of the integration error as afunction of the difference between calculated flowrates.

FIG. 8 shows a similar plot comparing a single diameter path against the4-chord configuration for the same two distorted profiles of FIG. 7.There is a much poorer correlation between the difference value and theintegration error in the 4-path meter. Therefore, the approachillustrated by FIG. 7 using the three- and four-chord schemes is moreeffective at detecting and quantifying integration errors than is theapproach using a 4-chord and single-path scheme as illustrated by FIG.8. The example above uses locations for the chordal planes and weighingfactors that correspond with the abscissa and weights of an appropriateintegration rule. Any two of a variety of integration methods may beused for the first and second integration methods. Gauss-Legendre andGauss-Jacobi are two well-known integration rules, the Anti-Gauss-Jacobirule is a less well-known rule. Other integration schemes may be used,such as the Optimal Weighted Integration for Circular Sections (“OWICS”)scheme optimized especially for flow measurement purposes.

As an alternative to these rules that have pre-defined abscissa, similarmethodologies can be applied where the chord locations (of at least oneof the two alternative subsets) are selected arbitrarily or based onother considerations and then the weighing factors are calculatedaccordingly. In one such possible scheme, four chordal locations couldbe selected according to the rules of a first integration method with aneven number of abscissas, and a fifth chordal plane could be added inthe central diametric plane. For the first integration the standard4-chord weighting factors would be applied and the diametric chord wouldbe ignored, and for the second integration a new set of non-zeroweighting factors would be applied to all five chordal velocity inputs.

A preferred embodiment of a method of detecting integration errors—themethod being performed by a non-transitory computer readable medium withcomputer instructions stored thereon executed by a processor—includesthe step of: executing a first chordal integration scheme and a seconddifferent chordal integration scheme, the chordal integration schemessharing at least one chordal path in a discrete chordal measurementplane across a conduit section of the meter body. The total number ofchordal paths (and planes) is less than a sum of the chordal paths (andplanes) used in the first and second different chordal integrationschemes. Path locations and weighting factors of one of the first andsecond different chordal integration schemes can correspond with anabscissa and weights of a numerical integration scheme withpre-determined abscissae. Alternatively, path locations can be selectedindependent of an abscissa and weights of a numerical integration schemewith pre-determined abscissae, with appropriate weighting factors beingcalculated for those paths.

One of the chordal integration schemes can be implemented in the form

${\overset{\_}{v}}_{a} = {\sum\limits_{i = 1}^{N}\; {w_{a,i}{v\left( h_{a,i} \right)}}}$$Q_{a} = {{{\overset{\_}{v}}_{a}A} = {A{\sum\limits_{i = 1}^{N}\; {w_{a,i}{v\left( h_{a,i} \right)}}}}}$

with the other chordal integration schemes implemented in the form

${\overset{\_}{v}}_{b} = {\sum\limits_{j = 1}^{M}\; {w_{b,j}{v\left( h_{b,j} \right)}}}$$Q_{b} = {{{\overset{\_}{v}}_{b}A} = {A{\sum\limits_{j = 1}^{M}\; {w_{b,j}{v\left( h_{b,j} \right)}}}}}$

wherein the total number of chordal measurement planes P is less thanthe sum of N plus M such that at least one of the chordal measurementplanes at location h_(a,i) is the same as one of the chordal measurementplanes at locations h_(b,j).

The preferred embodiments described here are for illustrative purposes.The scope of the invention is defined by the following claims andincludes the full range of equivalents to the elements recited.

What is claimed:
 1. A method of detecting integration errors, the methodbeing performed by at least one set of computational electronicsincluding a non-transitory computer readable medium with computerinstructions stored thereon executed by a processor, the methodcomprising the steps of: executing a first chordal integration schemeand a second different chordal integration scheme, at least one chordalpath being common to the first and second different chordal integrationschemes; wherein the at least one chordal path lies in a discretechordal measurement plane across a conduit section of a meter body; andwherein a total number of chordal paths is less than a sum of thechordal paths used in the first and second different chordal integrationschemes.
 2. A method according to claim 1 further comprising the step ofselecting path locations and weighting factors of one of the first andsecond different chordal integration schemes to correspond with theabscissae and weights of a numerical integration scheme withpre-determined abscissae.
 3. A method according to claim 1 furthercomprising the step of selecting path locations of one of the first andsecond different chordal integration schemes independent of theabscissae and weights of a numerical integration scheme withpre-determined abscissae, and then calculating appropriate weightingfactors for those paths.
 4. The method according to claim 1 whereby oneof the chordal integration schemes is implemented in the form${\overset{\_}{v}}_{a} = {\sum\limits_{i = 1}^{N}\; {w_{a,i}{v\left( h_{a,i} \right)}}}$and another of the chordal integration schemes is implemented in theform${\overset{\_}{v}}_{b} = {\sum\limits_{j = 1}^{M}\; {w_{b,j}{v\left( h_{b,j} \right)}}}$wherein a total number of chordal measurement planes is less than thesum of N plus M such that at least one of the chordal measurement planesat location h_(a,i) is the same as one of the chordal measurement planesat locations h_(b,j).
 5. A method according to claim 1 wherein one ofthe first and second different chordal integration schemes is anodd-numbered integration scheme and one is an even-numbered integrationscheme.
 6. A method according to claim 1 wherein the first and seconddifferent chordal integration schemes are both an odd-numberedintegration scheme.
 7. A method according to claim 1 wherein the firstand second different chordal integration schemes are both aneven-numbered integration scheme.
 8. A system for measuring a flow rateof a fluid using a meter body housing multiple ultrasonic transducers,each ultrasonic transducer being used in conjunction with at least oneother ultrasonic transducer to form a chordal path in a discrete chordalmeasurement plane across a conduit section of the meter body; the systemcomprising: at least one set of computational electronics including anon-transitory computer readable medium with computer executableinstructions executed by processor, the computer executable instructionsincluding a first chordal integration scheme and a second differentchordal integration scheme, at least one chordal path being common tothe first and second different chordal integration schemes.
 9. A systemaccording to claim 8 further comprising the first chordal integrationscheme and the second different chordal integration scheme using twosubsets of chordal measurement planes each with a summation that usesweighting factors that are dissimilar.
 10. A system according to claim 8wherein one of said chordal integration schemes is an odd-numberedintegration scheme and another of said chordal integration schemes is aneven-numbered integration scheme.
 11. A system according to claim 8wherein the chordal measurement plane contains two or more chordal pathsarranged at different angles to a conduit axis such that a chordalvelocity measurement in each chordal measurement plane can be madesubstantially independent of a non-axial flow velocity.